Fixed Points and Random Stability of a Generalized Apollonius Type Quadratic Functional Equation

In this paper, in the absence of any constraint qualifications, we develop sequential necessary and sufficient optimality conditions for a constrained multiobjective fractional programming problem characterizing a Henig proper efficient solution in terms of the ǫ-subdifferentials and the subdifferentials of the functions. This is achieved by employing a sequential Henig subdifferential calculus rule of the sums of m (m ≥ 2) proper convex vector valued mappings with a composition of two convex vector valued mappings. In order to present an example illustrating the main results of this paper, we establish the classical optimality conditions under Moreau-Rockafellar qualification condition. Our main results are presented in the setting of reflexive Banach space in order to avoid the use of nets.

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Strong Convergence Theorems for a Finite Family of Sequences of Nearly Nonexpansive Mappings in Hilbert Spaces

Tuyen

2018

Numerical Functional Analysis and Optimization

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Fixed Points and Random Stability of a Generalized Apollonius Type Quadratic Functional Equation

Abstract: Using the fixed-point method, we prove the generalized Hyers-Ulam stability of a generalized Apollonius type quadratic functional equation in random Banach spaces.

Cited by 5 publications

References 43 publications

Continuous Multiobjective Programming

Continuous Multiobjective Programming

Sequential approximate weak optimality conditions for multiobjective fractional programming problems via sequential calculus rules for the Brøndsted-Rockafellar approximate subdifferential

Strong Convergence Theorems for a Finite Family of Sequences of Nearly Nonexpansive Mappings in Hilbert Spaces

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