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In this paper, we present some inequalities involving k-gamma and k-beta functions via some classical inequalities, like Chebyshev's inequality for synchronous (asynchronous) mappings, Grüss', and Ostrowski's inequality. Also, we give applications of k-beta function in probability distributions. Most of the inequalities produced in this paper are the k-analogs of existing results. If k = 1,we have the classical one. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a multi-step hybrid extragradient algorithm by combining Korpelevich's extragradient method, the viscosity approximation method, the hybrid steepest-descent method, Mann's iteration method and the gradient-projection method (GPM) with regularization in the setting of infinite-dimensional Hilbert spaces. It is proven that, under appropriate assumptions, the proposed algorithm converges strongly to a solution of the convex minimization problem (CMP) with constraints of several problems: finitely many generalized mixed equilibrium problems (GMEPs), finitely many variational inclusions, and the fixed point problem of a strictly pseudocontractive mapping. In the meantime, we also prove the strong convergence of the proposed algorithm to the unique solution of a hierarchical variational inequality problem (over the fixed point set of a strictly pseudocontractive mapping) with constraints of finitely many GMEPs, finitely many variational inclusions and the CMP. The results presented in this paper improve and extend the corresponding results announced by many others. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of solutions for a variational-like inequality and a generalized variational-like inequality in the relaxed η-α pseudomonotone and strictly η-quasimonotone cases in Banach spaces by using the KKM technique. The results presented in this paper improve and extend some corresponding results of several authors. [ABSTRACT FROM AUTHOR]

In this paper, we study the blow-up singularity of a semilinear parabolic equation with nonlinear memory both in the reaction term and the boundary condition. We firstly establish the local solvability for a large class of semilinear parabolic equations with various nonlocal reaction terms. Secondly, we give a complete classification for the existence of a blow-up solution and a global solution. Next, we show that under some hypotheses the blow-up can only occur on the boundary of the domain. [ABSTRACT FROM AUTHOR]

In this paper, multi-valued version of SCC, SKC, KSC, and CSC conditions in Ptolemy metric space are presented. Then the existence of a fixed point for these mappings in a Ptolemy metric space are proved. Finally, some examples are presented. [ABSTRACT FROM AUTHOR]

In this paper, we obtain an inequality for the normalized Casorati curvature of slant submanifolds in quaternionic space forms by using T Oprea's optimization method. [ABSTRACT FROM AUTHOR]

In this paper, by using a nonlinear scalarization technique, we obtain sufficient conditions for Hölder continuity of the solution mapping for a parametric generalized vector quasi-equilibrium problem with set-valued mappings. The results are different from the recent ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of the rank game and propose a mathematical model for it. By a discrete fixed point theorem, we give the existence results of rank equilibria. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the double inequality Mp(a, b) < U(a, b) < Mq(a, b) holds for all a, b > 0 with a ≠ b if and only if p ≤ 2 log 2/(2 logπ - log 2) = 0.8684 ⋯ and q ≥ 4/3, where U(a, b) and Mr (a, b) are the Yang and rth power means of a and b, respectively. [ABSTRACT FROM AUTHOR]