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We introduce the modified Picard–Ishikawa hybrid iterative scheme and establish some strong convergence results for the class of asymptotically generalized ϕ-pseudocontractive mappings in the intermediate sense in Banach spaces and approximate the fixed point of this class of mappings via the newly introduced iteration scheme. We construct some numerical examples to support our results. Furthermore, we apply the Picard–Ishikawa hybrid iteration scheme in solving the nonlinear Caputo type fractional differential equations. Our results generalize, extend and unify several existing results in literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence and uniqueness of common fixed point of tower type contractive mappings in complete metric (pseudo)modular spaces involving the theoretic relation. However, the newly introduced contraction in this paper further characterize and includes in their full strength several existing results in metrical fixed point theory. Some nontrivial supportive examples were given to justify our result. Our results generalize, improve, and unify some existing results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new fixed point iterative scheme called the AG iterative scheme that is used to approximate the fixed point of a contraction mapping in a uniformly convex Banach space. The iterative scheme is used to prove some convergence result. The stability of the new scheme is shown. Furthermore, weak convergence of Suzuki's generalized non-expansive mapping satisfying condition (C) is shown. The rate of convergence result is proved and it is demonstrated via an illustrative example which shows that our iterative scheme converges faster than the Picard, Mann, Noor, Picard-Mann, M and Thakur iterative schemes. Data dependence results for the iterative scheme are shown. Finally, our result is used to approximate the solution of a nonlinear fractional differential equation of Caputo type. [ABSTRACT FROM AUTHOR]

We approximate the fixed point of the Suzuki's generalized nonexpansive mappings via the Picard-Ishikawa hyprid iterative process, recently introduced by Okeke [18]. We prove some weak and strong convergence theorems of this type of mappings in the setting of uniformly convex Banach spaces. We apply our results in finding the solution of a mixed type Volterra-Fredholm functional nonlinear integral equation in Banach spaces. Finally, we give several numerical examples to validate our analytical results. Our results extend and improve several known results in literature, including the results of Okeke [18], Ullah and Arshad [30] and Craciun and Serban [7] among others. [ABSTRACT FROM AUTHOR]

Purpose - This paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. Furthermore, the authors produce an example to demonstrate the applicability of the results. Design/methodology/approach - The results of this paper are theoretical and analytical in nature. Findings - The authors established some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. An example was constructed to demonstrate the applicability of the results. Research limitations/implications - Analytical and theoretical results. Practical implications - The results of this paper can be applied in science and engineering. Social implications - The results of this paper is applicable in certain social sciences. Originality/value - The results of this paper are new and will open up new areas of research in mathematical sciences. [ABSTRACT FROM AUTHOR]