In this paper, we define F-contractive type mappings in b-metric spaces and prove some fixed point results with suitable examples. F-expanding type mappings are also defined and a fixed point result is obtained.

In this paper, we introduce a new class of generalized nonexpansive mappings which is wider than the class of mappings satisfying (C) condition. Different properties and some fixed point results for these mappings are obtained here. The convergence of some iteration schemes to the fixed point is also discussed with suitable examples.

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For two real Banach algebras $\mathbb{A}_1$ and $\mathbb{A}_2$, let $K_p$ be the projective cone in $\mathbb{A}_1\otimes_\gamma \mathbb{A}_2$. Using this we define a cone norm on the algebraic tensor product of two vector spaces over the Banach algebra $\mathbb{A}_1\otimes_\gamma \mathbb{A}_2$ and discuss some properties. We derive some fixed point theorems in this projective cone normed tensor product space over Banach algebra with a suitable example. For two self mappings $S$ and $T$ on a cone Banach space over Banach algebra, the stability of the iteration scheme $x_{2n+1}=Sx_{2n}$, $x_{2n+2}=Tx_{2n+1},\;n=0,1,2,...$ converging to the common fixed point of $S$ and $T$ is also discussed here.

mapping on P ⊗Q. Using T1 and T2 we define a self mapping T on X ⊗γ Y . Different conditions under which T + T S + S has a fixed point in P ⊗ Q are established here. Analogous results are also established taking the pair (T1, T2) as (k, k / ) contraction mappings. Again considering X ⊗γ Y as a reflexive Banach space. We derive the conditions for 1 m (T + ST + S), m > 2, m ∈ N, for having a fixed point in P ⊗ Q. Some iteration schemes converging to a fixed point of T + ST + S in P ⊗ Q are also presented here.

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The aim of this paper is to introduce a new class of generalized centralizers on [Formula: see text]-algebras which is termed as extended [Formula: see text]-centralizer. We study different properties of this class of centralizers. Moreover, we define a class of [Formula: see text]-algebras which contains the prime [Formula: see text]-algebras as a subclass. Different properties of extended centralizers with respect to this class of [Formula: see text]-algebras are discussed with suitable examples.

In this paper, we introduce an extended S-iteration scheme for G-contractive type mappings and prove ∆-convergence as well as strong convergence in a nonempty closed and convex subset of a uniformly convex and complete b-metric space with a directed graph. We also give a numerical example in support of our result and compare the convergence rate between the studied iteration and the modified S-iteration.