Random fixed point theorem for multivalued nonexpansive operators in Uniformly nonsquare Banach spaces

Abstract

Let (Ω, Σ) be a measurable space, with a sigma-algebra of subset of Ω, and let C be a nonempty bounded closed convex and separable subset of a Banach space X, satisfying Dominguez-Lorenzo condition, KC(X) the family of all compact convex subsets of X. We prove that a 1-χ contractive mutivalued nonexpansive random operator from C into KC(X) satisfying an inwardness condition has a random fixed point. Furthermore, we also prove that a uniformly nonsquare Banach spaces with property WORTH has a random fixed point for multivalued nonexpansive non-self random operators.

Generalized Random α-ψ-Contractive Mappings with Applications to Stochastic Differential Equation

“…In 1984, Sehgal and Waters [8] proved the random fixed point theorem versions of the well-known Rothe's fixed point theorem. Since then, many improvements of random fixed point theorems have been established in the literature in several ways; see for example [9][10][11][12][13][14][15]. It is the most widely-applied random fixed point result in different areas of mathematics, statistics, engineering, and physics, among other.…”

Generalized Random α-ψ-Contractive Mappings with Applications to Stochastic Differential Equation

“…In 1984, Sehgal and Waters [8] proved the random fixed point theorem versions of the well-known Rothe's fixed point theorem. Since then, many improvements of random fixed point theorems have been established in the literature in several ways; see for example [9][10][11][12][13][14][15]. It is the most widely-applied random fixed point result in different areas of mathematics, statistics, engineering, and physics, among other.…”

Random Best Proximity Points for α-Admissible Mappings via Simulation Functions

“…In 1984, Sehgal and Waters [7] proved the random fixed point theorem of the classical Rothe's fixed point theorem. After that, many authors have extended, generalized and improved random fixed point theorems in several ways [8][9][10][11][12][13][14][15][16].…”

Random fixed point theorems for Hardy-Rogers self-random operators with applications to random integral equations

“…Recently, Beg and Shahzad [4] showed the existence of random common fixed points and random coincidence points of a pair of compatible random multi-valued mappings in Polish spaces. Especially, Kumam et al [14][15][16][17][18] proved many random fixed point theorems for multi-valued nonexpansive nonself-mappings satisfying the inwardness condition in Banach spaces (see [19]). Jung et al [13] proved random fixed point theorems for a certain class of mappings in banach spaces.…”

Generalized Random α-ψ-Contractive Mappings with Applications to Stochastic Differential Equation

“…In 1984, Sehgal and Waters [8] proved the random fixed point theorem versions of the well-known Rothe's fixed point theorem. Since then, many improvements of random fixed point theorems have been established in the literature in several ways; see for example [9][10][11][12][13][14][15]. It is the most widely-applied random fixed point result in different areas of mathematics, statistics, engineering, and physics, among other.…”

Random Best Proximity Points for α-Admissible Mappings via Simulation Functions

“…In 1984, Sehgal and Waters [7] proved the random fixed point theorem of the classical Rothe's fixed point theorem. After that, many authors have extended, generalized and improved random fixed point theorems in several ways [8][9][10][11][12][13][14][15][16].…”

Random fixed point theorems for Hardy-Rogers self-random operators with applications to random integral equations

“…Recently, Beg and Shahzad [4] showed the existence of random common fixed points and random coincidence points of a pair of compatible random multi-valued mappings in Polish spaces. Especially, Kumam et al [14][15][16][17][18] proved many random fixed point theorems for multi-valued nonexpansive nonself-mappings satisfying the inwardness condition in Banach spaces (see [19]). Jung et al [13] proved random fixed point theorems for a certain class of mappings in banach spaces.…”

Generalized Random α-ψ-Contractive Mappings with Applications to Stochastic Differential Equation

“…In 1984, Sehgal and Waters [8] proved the random fixed point theorem versions of the well-known Rothe's fixed point theorem. Since then, many improvements of random fixed point theorems have been established in the literature in several ways; see for example [9][10][11][12][13][14][15]. It is the most widely-applied random fixed point result in different areas of mathematics, statistics, engineering, and physics, among other.…”

Random Best Proximity Points for α-Admissible Mappings via Simulation Functions

“…In 1984, Sehgal and Waters [7] proved the random fixed point theorem of the classical Rothe's fixed point theorem. After that, many authors have extended, generalized and improved random fixed point theorems in several ways [8][9][10][11][12][13][14][15][16].…”

Random fixed point theorems for Hardy-Rogers self-random operators with applications to random integral equations

“…Recently, Beg and Shahzad [4] showed the existence of random common fixed points and random coincidence points of a pair of compatible random multi-valued mappings in Polish spaces. Especially, Kumam et al [14][15][16][17][18] proved many random fixed point theorems for multi-valued nonexpansive nonself-mappings satisfying the inwardness condition in Banach spaces (see [19]). Jung et al [13] proved random fixed point theorems for a certain class of mappings in banach spaces.…”