In this paper, we will use the notion of α-admissible mappings in Banach spaces, to introduce concept Tβ-contractive and establish a fixed point theorem for type contractions. Our theorems generalize improve many results literature. Moreover, apply main result prove existence solution Volterra-integral equation, under more general assumptions than previously made.

Let $ H$ be a Hilbert space and $C$ be a closed, convex and nonempty subset of $H$. Let $T:C rightarrow H$ be a non-self and non-expansive mapping. V. Colao and G. Marino with particular choice of the sequence  ${alpha_{n}}$ in Krasonselskii-Mann algorithm, ${x}_{n+1}={alpha}_{n}{x}_{n}+(1-{alpha}_{n})T({x}_{n}),$ proved both weak and strong converging results. In this paper, we generalize thei...

In this paper, we introduce the new notion of contravariant (α−ψ) Meir–Keeler contractive mappings by defining α-orbital admissible and covariant contraction in bipolar metric spaces. We prove fixed point theorems for these contractions also provide some corollaries main results. An example is be given support our result. end, solve an integral equation using

In this work, we establish new fixed point theorems for generalized Pata–Suzuki type contraction via α -admissible mapping in metric spaces and to prove some results such mappings. Moreover, give an example illustrate our main result. Consequently, the presented paper generalize improve corresponding of literature.

In this paper, our focus is to acquaint with the Suzuki-type mappings establish some fixed point results using new w-interpolative approach. We present for interpolative contraction operators via w-admissible maps which satisfy Kannan, ?iri?–Reich–Rus, and Hardy–Rogers contractions in quasi-partial b-metric space. Further, outcomes so obtained are affirmed relevant examples.

In this paper, we introduce the notion of generalized (α, φ, ψ)- Geraghty contractive type mappings in setup Sb-metric spaces and α-orbital admissible with respect to φ. Furthermore, fixed-point theorems for such complete are proven without assuming subadditivity ψ. Some examples provided supporting our main results. Also, gave an application integral equations as well Homotopy.

martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. in this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.