A q-VARIANT OF STEFFENSEN'S METHOD OF FOURTH-ORDER CONVERGENCE

Starting from q-Taylor formula, we suggest a new q-variant of Stef-fensen's method of fourth-order convergence for solving non-linear equations

Fixed Points on Covariant and Contravariant Maps with an Application

Fixed-point results on covariant maps and contravariant maps in a (Formula presented.) -algebra-valued bipolar metric space are proved. Our results generalize and extend some recently obtained results in the existing literature. Our theoretical results in this paper are supported with suitable examples. We have also provided an application to find an analytical solution to the integral equation and the electrical circuit differential equation. © 2022 by the authors

Fixed point theorem on an orthogonal extended interpolative ψF-contraction

In this paper, we establish the fixed point results for an orthogonal extended interpolative Ciric Reich-Rus type $\psi\mathcal{F}$-contraction mapping on an orthogonal complete $\mathfrak{b}$-metric spaces and give an example to strengthen our main results. Furthermore, we present an application to fixed point results to find analytical solutions for functional equation

Some Novel Inequalities for LR-(k,h-m)-p Convex Interval Valued Functions by Means of Pseudo Order Relation

In this paper, a new type of convexity is defined, namely, the left–right-(k,h-m)-p IVM (set-valued function) convexity. Utilizing the definition of this new convexity, we prove the Hadamard inequalities for noninteger Katugampola integrals. These inequalities generalize the noninteger Hadamard inequalities for a convex IVM, (p,h)-convex IVM, p-convex IVM, h-convex, s-convex in the second sense and many other related well-known classes of functions implicitly. An apt number of numerical examples are provided as supplements to the derived results

Riemann-Liouville Fractional Inclusions for Convex Functions Using Interval Valued Setting

In this work, various fractional convex inequalities of the Hermite–Hadamard type in the interval analysis setting have been established, and new inequalities have been derived thereon. Recently defined p interval-valued convexity is utilized to obtain many new fractional Hermite–Hadamard type convex inequalities. The derived results have been supplemented with suitable numerical examples. Our results generalize some recently reported results in the literature

Riemann-Liouville Fractional Inclusions for Convex Functions Using Interval Valued Setting

In this work, various fractional convex inequalities of the Hermite–Hadamard type in the interval analysis setting have been established, and new inequalities have been derived thereon. Recently defined p interval-valued convexity is utilized to obtain many new fractional Hermite–Hadamard type convex inequalities. The derived results have been supplemented with suitable numerical examples. Our results generalize some recently reported results in the literature

Some Novel Inequalities for LR-(k,h-m)-p Convex Interval Valued Functions by Means of Pseudo Order Relation

In this paper, a new type of convexity is defined, namely, the left–right-(k,h-m)-p IVM (set-valued function) convexity. Utilizing the definition of this new convexity, we prove the Hadamard inequalities for noninteger Katugampola integrals. These inequalities generalize the noninteger Hadamard inequalities for a convex IVM, (p,h)-convex IVM, p-convex IVM, h-convex, s-convex in the second sense and many other related well-known classes of functions implicitly. An apt number of numerical examples are provided as supplements to the derived results

An Application to Fixed-Point Results in Tricomplex-Valued Metric Spaces Using Control Functions

In the present work, we establish fixed-point results for a pair of mappings satisfying some contractive conditions on rational expressions with coefficients as point-dependent control functions in the setting of tricomplex-valued metric spaces. The proven results are extension and generalisation of some of the literature’s well-known results. We also explore some of the applications to our key results

An Application of Urysohn Integral Equation via Complex Partial Metric Space

Metric fixed point theory has vast applications in various domain areas, as it helps in finding analytical solutions under various contractive conditions, including non-linear integral-type contractions. In our present work, we have established fixed point results in the setting of complex valued partial metric space. Our results extend the results proven in literature. Using our main result, we have provided an application to find the solution to the Urysohn-type integral equation

Solving an Integral Equation via Tricomplex-Valued Controlled Metric Spaces

In this present study, we propose the concept of tricomplex-controlled metric spaces as a generalization of both controlled metric-type spaces and tricomplex metric-type spaces. In this work, we establish fixed point results using Banach, Kannan and Fisher-type contractions supported with nontrivial examples in the setting of the proposed space. We apply the derived result to find the analytical solution of an integral equation using the fixed point technique under the same metric