Let R_n be the space of rational functions with prescribed poles. If r ∈ R_n, does not vanish in |z| < k, then for k = 1 $${\mid}r^{\prime}(z){\mid}{\leq}{\frac{{\mid}B^{\prime}(z){\mid}}{2}}\sup_{z{\in}T}{\mid}r(z){\mid}$$, where B(z) is the Blaschke product. In this paper, we consider a more general class of rational functions rof ∈ R_m*n, defined by (rof)(z) = r(f(z)), where f(z) is a polynomial of degree m^* and prove a more general result of the above inequality for k > 1. We also prove that $$\sup_{z{\in}T}\left[\left|{\frac{r^{*\prime}(f(z)}{B^{\prime}(z)}}\right|+\left|{\frac{r^{\prime}(f(z))}{B^{\prime}(z)}}\right|\right]=\sup_{z{\in}T}\left|{\frac{(rof)(z)}{f^{\prime}(z)}}\right|$$, and as a consequence of this result, we present a generalization of a theorem of O'Hara and Rodriguez for self-inverse polynomials. Finally, we establish a similar result when supremum is replaced by infimum for a rational function which has all its zeros in the unit circle.

In this paper, we extend the concept of S-contractions of type E in an S-metric space. Further, by combining simulation function and S-contractions of type E, we examine the existence and uniqueness of fixed point in a complete S-metric space. Sufficient examples are provided and application to the solution of integral equation is also made.

This paper explores the significance and implications of fixed point results related to orbital contraction as a novel form of contraction in various fields. Theoretical developments and theorems provide a solid foundation for understanding and utilizing the properties of orbital contraction, showcasing its efficacy through numerous examples and establishing stability and convergence properties. The application of orbital contraction in control systems proves valuable in designing resilient and robust control strategies, ensuring reliable performance even in the presence of disturbances and uncertainties. In the realm of financial modeling, the application of fixed point results offers valuable insights into market dynamics, enabling accurate price predictions and facilitating informed investment decisions. The practical implications of fixed point results related to orbital contraction are substantiated through empirical evidence, numerical simulations, and real-world data analysis. The ability to identify and leverage fixed points grants stability, convergence, and optimal system performance across diverse applications.

In this paper, we propose a modified Halpern's iterative scheme developed from a sequence of a new class of enriched nonspreading mappings and an enriched nonexpansive mapping in the setup of a real Hilbert space. Moreover, we prove strong convergence theorem of the proposed method under mild conditions on the control parameters. Also, we obtain some basic properties of our new class of enriched nonspreading mappings.

This study develops an optimal control strategy for canine rabies transmission using a two-dimensional spatiotemporal model with spatial dynamics. Our objective is to minimize the number of infected and exposed individuals while reducing vaccination costs. We rigorously establish the existence of optimal control and provide a detailed characterization. Numerical simulations show that early intervention, in particular timely vaccination at the onset of an outbreak, effectively controls the disease. Our model highlights the importance of spatial factors in rabies spread and underlines the need for proactive vaccination campaigns, providing valuable insights for public health policy and intervention strategies.

In this paper, we study the existence and uniqueness of solutions for a class of fractional differential inclusion including a maximal monotone operator in real space with an initial condition. The main results of the existence and uniqueness are obtained by using resolvent operator techniques and multivalued fixed point theory.

In this paper, we developed the existence and uniqueness results by monotone method for non-linear fractional reaction-diffusion equation together with initial and boundary conditions. In this text the Hilfer fractional derivative is used to denote the time fractional derivative. The employment of monotone method generates two sequences of minimal and maximal solutions which converges to lower and upper solutions respectively.

In this paper, we introduce the new concept of 𝜓_s-rational type contractive mapping in the sense of 𝑏-metric spaces. Also, we obtain some fixed point results for these contractive mappings in complete b-metric spaces. Our main results generalize, extend and improve the corresponding results on the topics given in the literature. Finally, we also give some examples to illustrate our main results.

In this paper, we propose an inertial method for solving a common solution to fixed point and Variational Inequality Problem in Hilbert spaces. Under some standard and suitable assumptions on the control parameters, we prove that the sequence generated by the proposed algorithm converges strongly to an element in the solution set of Variational Inequality Problem associated with a quasimonotone operator which is also solution to a fixed point problem for a demimetric mapping. Finally, we give some numerical experiments for supporting our main results and also compare with some earlier announced methods in the literature.

In this paper, we study the existence and uniqueness of solutions for the fractional time-varying delay integrodifferential equation with multi-point multi-term nonlocal and fractional integral boundary conditions by using fixed point theorems. The fractional derivative considered here is in the Caputo sense. Examples are provided to illustrate the results.

A new type of more general form of variational inequalities for quasi-pseudo-monotone type III and strong quasi-pseudo-monotone type III operators has been obtained on compact domains in locally convex Hausdorff topological vector spaces. These more general forms of variational inequalities for the above types of operators used the more general form of minimax inequality by Chowdhury and Tan in [3] as the main tool to derive them. Our new results established in this paper should have potential applications in nonlinear analysis and related applications, e.g., see Aubin [1], Yuan [11] and references wherein.

In this research, we propose a new efficient iterative method for fixed point problems of generalized α-nonexpansive mappings. We show the weak and strong convergence analysis of the proposed method under some mild assumptions on the control parameters. We consider the application of the new method to some real world problems such as convex minimization problems, image restoration problems and impulsive fractional differential equations. We carryout a numerical experiment to show the computational advantage of our method over some well known existing methods.

The objective of this article is to study the general set-valued nonlinear variational-hemivariational inequalities and investigate the gap function, regularized gap function and Moreau-Yosida type regularized gap functions for the general set-valued nonlinear variational-hemivariational inequalities, and also discuss the error bounds for such inequalities using the characteristic of the Clarke generalized gradient, locally Lipschitz continuity, inverse strong monotonicity and Hausdorff Lipschitz continuous mappings.

The purpose of this paper is to introduce a class of distance altering functions that establish the existence and uniqueness of fixed points of 𝜈-admissible mappings that are subject to a generalized (𝜓, 𝜑)-almost weakly contraction on a generalized b₂-metric space.

The objective of this paper is to ascertain the existence and uniqueness of common fixed point for four self mappings in intuitionistic Menger metric spaces under some conditions extending to (CLR) property and C-class functions. Some illustrative examples are furnished, which demonstrate the validity of the hypotheses. As an application to our main result, we derive a common fixed point theorem for four self-mappings in metric space. Our results generalize several works, including [4], [20].

In this paper, we represent regular functions on ternary theory in the view of quaternion. By expressing quaternions using ternary number theory, a new form of regular function, called E-regular, is defined. From the defined regular function, we investigate the properties of the appropriate hyper-conjugate harmonic functions and corresponding Cauchy-Riemann equations by pseudo-complex forms.