Interpolative metric spaces were recently introduced by Karapinar et al., who established fixed point theorems in this framework. In this paper, we clarify their position within the hierarchy of generalized metric spaces by proving that every interpolative metric is, in fact, a bmetric. Building on this structural clarification, we investigate nonlinear contractions in the setting of bsuprametric spaces, a class that strictly generalizes bmetric spaces and naturally accommodates quadratic terms in the triangletype inequality. We establish a Matkowskitype fixed point theorem for generalized contractions of iri type in bsuprametric spaces. Our approach replaces the classical linear contraction coefficient with a control function θ ∈ Θ1, thereby strengthening the contraction framework while balancing this generality with the natural assumption that Picard orbits are bounded. This yields existence and uniqueness of fixed points and convergence of Picard iterates under conditions that extend beyond traditional Lipschitztype bounds. As corollaries, we recover weaker versions of several wellknown fixed point theorems, including results of Czerwik and Berzig, demonstrating that our framework unifies and generalizes earlier principles. For applications of interpolative contractions to integral and differential equations, we refer the reader to recent works in the literature, while emphasizing that the present paper is primarily structural and foundational. Overall, this work broadens the scope of fixed point theory in generalized metric spaces and highlights the structural role of boundedness in nonlinear contraction analysis.
This study aims to assess the stability of time-delayed variable fractional-order difference systems (Fvods). The study introduces new criteria for evaluating the stability of these modern types of systems. These criteria are derived by transforming the target system into its equivalent forms of Volterra systems of the convolution type. This research utilizes specific properties of the Z-transform method to formulate the required criteria. The accuracy of these results is confirmed through numerical verification using examples related to the stability of solutions within these systems.
This study investigates a novel class of boundary value problems governed by Caputo conformable fractional differential pantograph equations, characterized by a proportional delay of the form phi(gamma t), with 0 < gamma < 1. Such models effectively describe phenomena in physics, engineering, and biological systems that exhibit both memory effects and self-similar dynamics. We formulate a general nonlinear problem and establish the existence and uniqueness of solutions through fixed-point techniques, including Banachs contraction principle and Schauders fixed-point theorem, under appropriate assumptions on the nonlinear term Phi (x, phi(t), phi(gamma t)). Furthermore, the Ulam-Hyers stability of the proposed problem is analyzed, offering insights into the robustness of solutions with respect to perturbations in the initial data.
This article focuses on the study of fixed point theorems for PRESICS type contractive mappings within the framework of "soft metric spaces", particularly when the underlying parameter set is finite. By extending classical contraction principles, we establish rigorous existence and uniqueness results that broaden the current theory of soft metric spaces. The necessity of the imposed conditions is illustrated through carefully designed examples, demonstrating that these assumptions cannot, in general, be relaxed. In addition, explanatory remarks are included to clarify the scope and relevance of the results in relation to existing fixed point theorems. Furthermore, we explore potential applications in nonlinear analysis, showing how the developed theoretical framework can guarantee the existence, uniqueness, and iterative convergence of solutions to nonlinear problems under uncertainty. These findings not only generalize known results to a wider setting but also provide a foundation for future research and practical applications in mathematics and applied sciences.
The primary objective of this research work is to establish strong coupled fixed point results in multiplicative metric spaces using maximum and product types of cyclic coupled contractions. In support of our main results, we present trivial and nontrivial illustrative examples within the space. Furthermore, an application of the Lebesgue integral equation is provided in aid of the proposed work on multiplicative metric spaces. It has the potential to be extended in many directions in the context of different types of metric spaces, with different types of contractive conditions for nonlinear mappings, and with the application of different types of integral equations.
The present article introduces the notion of modified λ ψ φ −weak proximal contraction and utilizes it to establish the existence and uniqueness of tripled best proximity points, common tripled best proximity points for newly defined proximally fuzzy compatible mappings. Finally, n-tupled best proximity points theorem is also established. The definitions are supported by furnishing some illustrative examples.
. To approximate fixed points of Suzuki generalized nonexpansive mappings, this paper investigates a four-step iterative scheme. Within the framework of uniformly convex Banach spaces, we establish both weak and strong convergence results for the proposed method. Numerical experiments reveal that our iterative approach achieves faster convergence compared to several existing schemes designed for Suzukis generalized nonexpansive mappings. To support our theoretical results, we provide illustrative numerical examples and compute fixed points using MATLAB. As a practical application, we introduce a projection-based iterative process for solving split feasibility problems (SFP) in a Hilbert space setting. The results presented in this study are original and extend several related findings previously reported in the literature.
In this paper, we defined a new class of close to convex functions by Srivastava-Attiya operator relating with Gegenbauer Polynomials and determine the first few initial coefficient bounds and established the notable Fekete Szego inequalities. Further we determined Hankel determinants results. The outcomes of the results in this article and special cases open to further exploration are stated as corollaries.
The so-called non-Bazilevic functions have not been studied very extensively unlike the class of Bazilevic functions. Here we intend to introduce and study a new class of functions whose analytic characterization would be expressed as a convex combination of the class of non-Bazilevic functions and its Alexander transform characterization. The function class is defined using a differential operator which involves generalized M-series. The generalized M-series unifies two popular special functions namely generalized Gaussian hypergeometric function and Mittag-Leffler function, so our study will not only unify but also generalizes various well-known studies in univalent function theory. Estimates involving the initial coefficients of the functions having Maclaurin series, which belong to the defined function class are our main results. Some examples along with graphs have been used to establish the inclusion and closure properties. Also, we obtain the logarithmic and inverse coefficients for the defined function class.
This paper establishes sufficient conditions for the stochastic asymptotic stability (SAS) and uniform stochastic boundedness (USB) of solutions to a class of fourth-order stochastic delay differential equations. By defining an appropriate Lyapunov-Krasovskii functional (LKF), two new theorems are proved that guarantee these stability and boundedness properties. As an application of the theoretical findings, two illustrative examples are presented to demonstrate the effectiveness of the established criteria. Finally, the results provide a novel and meaningful contribution to the qualitative analysis of higher-order stochastic delay differential equations and are expected to support further theoretical developments and applied investigations.
. This paper introduces a novel Kannan-type F-contraction that extends Wardowskis F- contraction to ordered metric spaces.'. Our research expands the boundaries of fixed point theory by applying this innovative contraction to a broader class of spaces. Additionally, we develop a new approach to investigate common fixed points in incomplete metric spaces, assuming the metric space possesses the t-property. To demonstrate the practical significance of these findings, we provide a series of illustrative examples. The implications of our contributions are further underscored by their potential applications in mathematical analysis, particularly within the domain of fractional calculus.
We investigate composition operators that leave model spaces Q(theta) = H-2 e( )theta H-2 invariant, where theta is a finite Blaschke product of degree two or three with distinct zeros. While the general case of arbitrary degree was recently classified in Muthukumar-Sarkar-Undrakh [6], the argument there is group-theoretic and structural in nature. In contrast, the present work gives an explicit coefficient-by-coefficient computation that reveals how the underlying cyclic symmetry emerges in low degrees. In the quadratic and cubic cases, we show that the invariance condition forces the symbol phi to be either the identity or a rotation by a primitive root of unity, recovering the well-known cyclic structure in a direct algebraic way. These model computations provide a concrete illustration of the rigidity mechanism behind the general classification theorem.
.The present article introduces the notion of modified lambda(psi)(phi) -weak proximal contraction and utilizes it to establish the existence and uniqueness of tripled best proximity points, common tripled best proximity points for newly defined proximally fuzzy compatible mappings. Finally, n-tupled best proximity points theorem is also established. The definitions are supported by furnishing some illustrative examples.
This paper introduces a subclass of sense-preserving, complex-valued, harmonic univalent mappings using a generalized multiplier transform. The structural properties, such as sharp coefficient bounds required for a function to be in the defined class, are investigated. Inclusion relations under convolution, criteria for convex combinations, growth results, and the covering theorem are established. It is verified that the class is invariant under the Bernardi-Lib era-Livingston operator.
Reverse and forward order laws for closed range operators such as idempotent operators, normal operators, regular operators on the Hilbert spaces are studied. Basically, these laws are established for core inverse, Moore Penrose inverse and group inverse under certain necessary and sufficient conditions noticing the entries of matrix representations of operators using different Hilbert space decompositions. Some examples on the infinite dimensional Hilbert spaces are given. In addition, mixed-type results are obtained.
The main objective of this study is to obtain new fixed point resultsfor a generalized contraction mapping in the class of b-multiplicative metric spaces via a simulation function. In this direction, the significance of our results is supported by illustrated examples. The obtained results are then applied to ensure the existence of a solution for Caputo-type nonlinear fractional differential equations.
In this paper, we define a new class of functions with respect to (nu, kappa)-symmetric points involving the differential characterizations of biunivalent functions. The class is defined by expressing a combination of powers of analytic characterizations, associated with the well-known classes of starlike and convex function with respect to symmetric points. Estimates involving the initial coefficients of the functions having Maclaurin series, which belong to the defined function class are our main results. Further, we have obtained the Fekete-Szego inequality of the defined function class.
. Let E be a reflexive Banach space. This article investigates the solvability of a nonlinear quadratic functional integral inclusion (NQFII) with a feedback control on the real half-axis. Our investigation for the existence of solutions is found within the space BC(R+, epsilon) of bounded continuous functions on the real half-axis R+ and takes values in E beneath the assumption that the set-valued function F1 satisfy Lipschitz condition in epsilon. The base we depend on in this study is the procedure related with measure of noncompactness in the space BC(R+, epsilon) by a given norm of continuity and applying Darbo's fixed point theorem. Moreover, the paper explores various qualitative properties associated with these solutions for the given problem such as Hyers-Ulam stability and asymptotic stability. Also, an example is considered to illustrate the adequacy and significance of our results.
In this article, we introduce generalized Bernstein type operators with two shifted notes and study their approximation properties. First, we calculate some estimates for these operators. Further, we discuss convergence theorems and order of approximation in terms of Korovkin theorem and first order modulus of smoothness respectively. Next, we study pointwise approximation results in terms of Peetre's K-functional, second order modulus of smoothness, Lipschitz type space and r(th) order Lipschitz type maximal function. Lastly, weighted approximation results and statistical approximation theorems are proved.
We study Ishikawa iterations in the framework of A-statistical convergence. For continuous mappings on closed, convex, bounded subsets of Banach spaces, we prove that if {alpha(n)}(n=1)(infinity) and {beta(n)}(n=1)(infinity) satisfy appropriate A-statistical conditions and either iteration sequence converges A-statistically to p, then both converge A-statistically to p and T(p) = p. For contractions on bounded intervals with matrices having the density preservation property, we establish convergence to the unique fixed point. This extends A-statistical convergence results from Mann iteration to Ishikawa iteration.
