On a three-step iteration process for multivalued Reich-Suzuki type $$\alpha $$-nonexpansive and contractive mappings

Fixed Point Results on Multi-Valued Generalized (α,β)-Nonexpansive Mappings in Banach Spaces

“…For finding fixed points of these maps, we have provided the multi-valued version of the M-iteration and showed, by an example, that it is more effective than the other iterative schemes. Since multi-valued (α, β)-nonexpansive are more general than the multi-valued generalized α-nonexpansive and multi-valued Reich-Suzuki type nonexpansive maps, we conclude that our main outcome improves and extends the corresponding results of Iqbal et al [13] and Maldar et al [15].…”

“…Let the sequence {k n } be iteratively generated as in (5) and let p 0 ∈ F ix (J). In light of Lemma 9, since the sequence ||k n − p 0 || is nonincreasing, the constant c ≥ 0 defined by c = lim n→∞ ||k n − p 0 || (15) exists.…”

“…In 2019, Pandey et al [14] introduced the notion of β-Riech-Suzuki type nonexpansive selfmaps. Recently, Maldar et al [15] obtained the multi-valued version of these maps. In 2020, Ullah et al [16] defined generalized (α, β)-nonexpansive maps.…”

Convergence and Stability Analysis of a New Four-Step Fixed-Point Algorithm

“…Although iterative algorithms have a wide and dynamic literature, studies for these algorithms can be listed as determining the conditions under which the sequence to be obtained by using certain mapping classes will converge, comparing the convergence speeds, and performing data dependence and stability analysis [11][12][13][14][15].…”

"Existence and Uniqueness of Solutions of a Boundary Value Problem of Fractional Order via S-Iteration"

“…The problems of existence, uniqueness and other properties of solutions of special forms of BVP (1.1)-(1.2) and its variants have been studied by several researchers under variety of hypotheses by using different techniques (as in [1,3,11,12,15,16,17,18,19,20,21,31,32]). Recently, S. Soltuz and T. Grosan [36] have studied the special version of equation (1.1).…”