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

Abstract

In this paper, we prove some random fixed point theorems for Hardy-Rogers self-random operators in separable Banach spaces and, as some applications, we show the existence of a solution for random nonlinear integral equations in Banach spaces. Some stochastic versions of deterministic fixed point theorems for Hardy-Rogers self mappings and stochastic integral equations are obtained.2010 Mathematics Subject Classification. 60H25, 47H09, 47H10, 41A50.

Several Fixed Point Theorems in Convex b-Metric Spaces and Applications

“…It is obvious that (H, d b , w) is a complete convex b-metric space with s = 2. Combining (10) and (11)…”

“…In the last few decades one could observe a huge amount of interest for the development of the fixed point theory because of plenty of applications, especially in metric spaces [1,2]. Banach's contraction principle [3] is one of the most widely applied fixed point theorems in all branches of mathematics [4][5][6][7][8][9][10][11][12]. In recent decades, scholars have devoted themselves to extending the above theorem to all kinds of generalized metric spaces [13][14][15][16][17].…”

Some Random Fixed-Point Theorems for Weakly Contractive Random Operators in a Separable Banach Space

“…In the recent past, random differential equations and random integral equations have been solved by random fixed-point theorems (see, for example, [12][13][14][15][16]). For some important contributions in the random fixedpoint theory, we invite the reader to consult [17][18][19][20][21][22][23][24][25] and the references therein.…”

General methods for bounding multidimensional ruin probabilities in regime-switching models

“…Moreover, for any i ∈ S, the sequences {D i n } n∈N and {U i n } n∈N converge monotonically, as n → ∞, to i with the exponential rate of convergence: A distinct mathematical methodology for obtaining the unique fixed point of the risk operator, based on Banach Contraction Principle, can be found in Gajek and Rudź [10]. Some stochastic developments of Banach-type fixed point theorems are discussed in Saipara et al [25]. Some asymptotic results for ruin probabilities can be found in Cheng and Yu [5], J. Peng and D. Wang [23], Guo et al [14], Yang and Li [29], Konstantinides and Li [16], Cai and Dickson [3], among others.…”