Random Implicit Hybrid Iterative Algorithms of Jungck-Type and Common Random Fixed Point Theorems with Stability Results
Abstract - Let be a separable Banach space, be a non-empty closed convex subset of and be a nonself random commuting mappings satisfying the generalized random - contractive-like operator , with and subspace of , with and . In this paper, a stochastic version of implicit hybrid iterative algorithm called a modified random implicit Jungck-Ishikawa and random implicit Jungck-Mann hybrid iterative algorithms are introduced and the unique common random fixed theorems are proved in the sense of two maps for a generalized random -contractive-like operators in a separable Banach space. Strong convergence results for random implicit Picard-Mann, random Picard iterative schemes for single map are deduced as corollaries. Stability results are also proved and an example is provided to demonstrate the applicability of the random hybrid schemes.
Keywords - Random implicit Jungck-Ishikawa iterative schemes, generalized random contractive-like operators, random weakly compatible maps, unique common random fixed point.
2010 Mathematics Subject Classification: 47H10, 54H25