In this note, we show that the recent results due to Khan and Oyetunbi [J. Fixed Point Theory Appl. 22:47, 2020], Górnicki [J. Fixed Point Theory Appl. 22:8, 2020], Bisht [J. Fixed Point Theory Appl. 21:54, 2019] and Górnicki [J. Fixed Point Theory Appl. 21:29, 2019] are still valid if mappings are not necessarily orbitally continuous or k-continuous on a complete metric space, but satisfy the weaker version of orbital continuity and k-continuity.
In the present work, we extend the semi-cyclic contraction conditions established by Gabeleh and Abkar [9] by introducing the concept of a p-semi-cyclic contraction for a pair of mappings (S,T) on the union of p(≥ 2) nonempty subsets in a Banach space. In the sequel, we establish several fundamental results, including existence and convergence theorems for best proximity points corresponding to the pair (S,T). Additionally, illustrative examples are provided to support our findings.
This paper is devoted to a Sturm-Liouville boundary value problem with two constant delays τ1,τ2 ∈ [π/3,π) and two potentials q1,q2 ∈ L2[0,π]. We derive an asymptotic expansion of the characteristic function and obtain asymptotic formulas for the eigenvalues. Using the Lidskii-Sadovnichii contour integration method, we establish an explicit formula for the first regularized trace of the corresponding operator.
The subject of this paper is a mathematical framework that provides a basis and a tool for reasoning about uncertainty based on linguistic information.
In this paper we study the existence of solutions for the nonlinear Sobolev type fractional partial integrodifferential equations with Neumann boundary condition. Under suitable assumptions the results are established by using the Leray-Schauder fixed point theorem.
