Modified Proximal point algorithms for finding a zero point of maximal monotone operators, generalized mixed equilibrium problems and variational inequalities
Copyright policy )Modified Proximal point algorithms for finding a zero point of maximal monotone operators, generalized mixed equilibrium problems and variational inequalities
En este artículo, demostramos teoremas de convergencia fuertes y débiles de algoritmos de punto proximal modificados para encontrar un elemento común del punto cero de operadores monótonos máximos, el conjunto de soluciones de problemas de equilibrio mixto generalizados, el conjunto de soluciones de problemas de desigualdad variacional y el conjunto de puntos fijos de asignaciones relativamente no expansivas en un espacio de Banach en condiciones diferentes. Nuestros resultados modifican y mejoran el resultado anterior de Li y Song. Clasificación de asignaturas de matemáticas 2000: 47H09; 47H10.
Dans cet article, nous prouvons des théorèmes de convergence forts et faibles d'algorithmes de point proximal modifiés pour trouver un élément commun du point zéro des opérateurs monotones maximaux, l'ensemble des solutions de problèmes d'équilibre mixte généralisés, l'ensemble des solutions de problèmes d'inégalité variationnelle et l'ensemble de points fixes de mappages relativement non expansés dans un espace de Banach dans des conditions de différence. Nos résultats modifient et améliorent le résultat précédent de Li et Song. Classification des matières mathématiques 2000: 47H09 ; 47H10.
In this article, we prove strong and weak convergence theorems of modified proximal point algorithms for finding a common element of the zero point of maximal monotone operators, the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems and the fixed point set of relatively nonexpansive mappings in a Banach space under difference conditions. Our results modify and improve previous result of Li and Song. Mathematics Subject Classification 2000: 47H09; 47H10.
في هذه المقالة، نثبت نظريات تقارب قوية وضعيفة لخوارزميات النقطة القريبة المعدلة لإيجاد عنصر مشترك لنقطة الصفر لمشغلي النغمة الرتيبة القصوى، ومجموعة حلول مسائل التوازن المختلط المعمم، ومجموعة حلول مسائل عدم المساواة التباينية ومجموعة النقاط الثابتة للتخطيطات غير التوسعية نسبيًا في مساحة بنك في ظل ظروف الاختلاف. تعمل نتائجنا على تعديل وتحسين النتيجة السابقة لكل من لي وسونغ. تصنيف مادة الرياضيات 2000: 47H09 ؛ 47H10.
Programming in abstract spaces, Economics, Fixed-Point Problems, Fixed Point Theorems in Metric Spaces, Discrete Mathematics and Combinatorics, Monotone operators and generalizations, Variational inequality, Numerical Analysis, Numerical Optimization Techniques, Fixed Point Theorems, Applied Mathematics, Iterative Algorithms for Nonlinear Operators and Optimization, Discrete mathematics, Variational inequalities, FOS: Philosophy, ethics and religion, Programming language, Computational Theory and Mathematics, Physical Sciences, Convergence (economics), Mathematics Subject Classification, generalised mixed equilibrium problems, Best Proximity Points, Convex Optimization, Geometry, Set (abstract data type), Space (punctuation), Mathematical analysis, proximal point algorithm, Iterative procedures involving nonlinear operators, Point (geometry), FOS: Mathematics, Economic growth, Banach space, Zero (linguistics), Pure mathematics, Linguistics, Fixed point, Applied mathematics, Computer science, strong convergence, Philosophy, Strongly monotone, Computer Science, FOS: Languages and literature, Monotone polygon, weak convergence, maximal monotone operators, Geometry and Topology, Analysis, Mathematics, Mixed-Integer Nonlinear Programs
Programming in abstract spaces, Economics, Fixed-Point Problems, Fixed Point Theorems in Metric Spaces, Discrete Mathematics and Combinatorics, Monotone operators and generalizations, Variational inequality, Numerical Analysis, Numerical Optimization Techniques, Fixed Point Theorems, Applied Mathematics, Iterative Algorithms for Nonlinear Operators and Optimization, Discrete mathematics, Variational inequalities, FOS: Philosophy, ethics and religion, Programming language, Computational Theory and Mathematics, Physical Sciences, Convergence (economics), Mathematics Subject Classification, generalised mixed equilibrium problems, Best Proximity Points, Convex Optimization, Geometry, Set (abstract data type), Space (punctuation), Mathematical analysis, proximal point algorithm, Iterative procedures involving nonlinear operators, Point (geometry), FOS: Mathematics, Economic growth, Banach space, Zero (linguistics), Pure mathematics, Linguistics, Fixed point, Applied mathematics, Computer science, strong convergence, Philosophy, Strongly monotone, Computer Science, FOS: Languages and literature, Monotone polygon, weak convergence, maximal monotone operators, Geometry and Topology, Analysis, Mathematics, Mixed-Integer Nonlinear Programs
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