In this paper we introduce and study the class of positive right (q,p) -mixing operators acting from Banach lattices into Banach spaces. These operators unify the notions of positive p -summing operators and classical (q,p) -mixing operators. We establish their basic properties and prove that they form a Banach operator ideal. Several inclusion theorems are obtained, together with stability results under composition. A Pietsch-type domination theorem is established and yields equivalent characterizations in terms of probability measures on the positive dual ball. We further derive factorization results and identify the relationship between positive right (q,p) -mixing operators, positive p -summing operators and p -concave operators.
In this paper, we aim to prove the existence of at least three solutions to Robin boundary problem with p(.)-triharmonic operator. The method is mainly related to a three critical points theorem from Ricceri. Moreover, we use some compact embedding theorems for variable exponent third-order Sobolev space.
For any positive integers ℓ , T_ℓ , k(n) denotes the number of k-tuple ℓ -regular partitions of an integer n. By employing q-identities, modular equations of degree 7 and continued fraction identities, we establish new congruence modulo 2, 3, 7. Our analysis is based on the continued fraction and a collection of associated q-identities and in particular we employ the modular and transformation properties of the continued fraction to derive explicit generating function dissections and establish the desired congruence relation.
In this paper, we propose a viscosity-type double inertial algorithm with self-adaptive stepsizes for solving non-monotone variational inequality problems involving uniformly continuous operators in real Hilbert spaces. The proposed method combines viscosity approximation and double inertial extrapolation techniques with a self-adaptive stepsize rule that does not require prior knowledge of the Lipschitz constant. Under suitable conditions, we establish a strong convergence of the generated sequence without assuming monotonicity, Lipschitz continuity, line-search procedures, or additional projection techniques. The obtained results extend several existing inertial and viscosity methods to a broader class of non-monotone and non-Lipschitz variational inequality problems. Numerical examples are presented to illustrate the effectiveness of the proposed algorithm.
We establish new parameter-dependent upper bounds for the numerical radius of 2× 2 operator matrices. The obtained estimates incorporate mixed product terms such as ω (BC) and ω (CB) , together with norm expressions involving the operator blocks, and refine several known numerical radius inequalities. We further study the associated optimization problems and determine optimal choices of the parameters that yield sharper bounds. As applications, we derive new numerical radius estimates for single operators and recover several known inequalities as special cases.
