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In the present paper, the aim is to obtain some new fixed point theorems for nonlinear F-contractions involving generalized distance to prove the existence of solution to second order differential equation related to conversion of solar energy to electrical energy. Non-trivial examples are also presented, to illustrate the obtained results and to s...
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... a basic understanding of how light is transformed into electricity, a mathematical model can be presented of the electric current in an RLC parallel circuit, also known as a tuning circuit (see [8]). In Figure 3, V is the voltage of the power source, I is the current in the circuit, R is the resistance of the resistor, L is the inductance of the inductor and C is the capacitance of the capacitor. Such problems are mathematically modeled as initial value problem for second order ordinary differential equation of the form : ...
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The terminal value problem of differential equations has an important application background. In this paper, we are concerned with the terminal value problem of a first-order differential equation. Some sufficient conditions are given to obtain the existence and uniqueness results of solutions to the problem. Firstly, some comparison lemmas are est...
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... Proof. Under assumptions (iv) and (v), the existence of a solution to the problem (4.5) follows from [19,Theorem 4.1]. Now, to prove the Lipschitz estimate (4.6), it suffices to apply Theorem 3.1. ...
This work deals with Lipschitz stability for a parametric version of the general second order Ordinary Differential Equation (ODE) initial-value Cauchy problem. We first establish a Lipschitz stability result for this problem under a partial variation of the data. Then, we apply our abstract result to second order differential equations governed by cocoercive operators. Furthermore, we discuss more concrete applications of the stability for two specific applied mathematical models inherent in electricity and control theory. Finally, we provide numerical tests based on the software source Scilab, which are done with respect to parametric linear control systems, illustrating henceforth the validity of our abstract theoretical result.
... Introduction/purpose: In this paper, several critical remarks are presented concerning the paper (Iqbal, 2020). Methods: Conventional theoretical methods of functional analysis. ...
... Note that (see, e.g., (Iqbal, 2020) or (Kadelburg, 2024)), for a w-distance p on a set X, the mapping ...
... In the recent paper (Iqbal, 2020), the authors tried to generalize the results of papers (Wardowski, 2012) and (Wardowski, 2018) in two waysfirstly, instead of metric d they used w-distance p or metric-like µ. On the other hand, instead of assumption (F1), the authors of (Iqbal, 2020) used the weaker assumption ...
Introduction/purpose: In this paper, several critical remarks are presented concerning the paper (Iqbal, 2020). Methods: Conventional theoretical methods of functional analysis. Results: It is shown that their use of non-decreasing "control" function F instead of strictly increasing one in Wardowski-type results usually produces contradictions.
... In some later papers (e.g., [11,16]), the authors used a stronger assumption, as follows: ...
... According to properties (p1), c) and d), the mapping q defined as in d) is a metric-like on the space X; see also [11,Remark 1.12]). e) w-distance is not necessarily a d-continuous function (in two variables). ...
... A lot of fixed point and common fixed point results in metric spaces endowed with a w-distance have been obtained by various authors (see, for example, the articles [11,16,17,[22][23][24] and, in particular, the book [20] and the references therein). ...
The aim of this paper is to present some new observations about w-distance (in the sense of O. Kada, T. Suzuki, W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japonica 44, 2 (1996), 381-391) and F-contractions (in the sense of D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94 (2012)). Both concepts have been examined separately a lot, but there have been few attempts to connect them. This article is a step in filling this gap. Besides, some comments and improvements of results in the existing literature are presented.
... Note that, see, e.g. (Iqbal & Rizwan, 2020) or (Kadelburg & Radenović, 2024), for a w-distance p on a set X, the mapping ...
... In the recent paper (Iqbal & Rizwan, 2020), the authors tried to generalize the results of papers (Wardowski, 2012) and (Wardowski, 2018) in two ways -firstly, instead of metric d they used w-distance p or metric-like µ. On the other hand, instead of the assumption (F1), the authors of (Iqbal & Rizwan, 2020) used the weaker assumption ...
... In the recent paper (Iqbal & Rizwan, 2020), the authors tried to generalize the results of papers (Wardowski, 2012) and (Wardowski, 2018) in two ways -firstly, instead of metric d they used w-distance p or metric-like µ. On the other hand, instead of the assumption (F1), the authors of (Iqbal & Rizwan, 2020) used the weaker assumption ...
Introduction/purpose: In this paper, several critical remarks are presented concerning the paper of Iqbal & Rizwan: Existence of the solution to second order differential equation through fixed point results for nonlinear F-contractions involving w0-distance from 2020. Methods: Conventional theoretical methods of functional analysis. Results: It is shown that their use of the non-decreasing "control" function F instead of a strictly increasing one in Wardowski-type results usually produces contradictions. Conclusion: It is shown that such results can be obtained in a more general class of metric-like spaces, where strict monotonicity is the only assumption that has to be imposed on the function F. An example is presented showing that the obtained results are stronger than the classic ones.
... • for any ε > 0, there exists δ > 0 such that w(x, y) ≤ δ and w(x, z) ≤ δ imply d(y, z) ≤ ε. Now we present some examples, which more explanations of them, can be found in some papers in the literature such as [10,11,14,16]. Example 1.1. ...
"In the present paper, we define the $Pw$-contraction by considering the inequality called $P$-contraction in metric space together with the $w$ -distance. We then present fixed point theorems for both single-valued and multivalued $Pw$-contractions. We also support our results with suitable examples."
... Very recently, Iqbal and Rizwan [25] considered a rich class of functions and generalized Definition 6 to obtain some new fixed point theorems for nonlinear F-contrac-tions involving generalized distance. On unifying the concept of Wardowski [10], Nadler [9] and Altun et al. [26] gave the concept of multivalued F-contraction as follows. ...
The aim of the paper is to discuss data dependence, existence of fixed points, strict fixed points, and well posedness of some multivalued generalized contractions in the setting of complete metric spaces. Using auxiliary functions, we introduce Wardowski type multivalued nonlinear operators that satisfy a novel class of contractive requirements. Furthermore, the existence and data dependence findings for these multivalued operators are obtained. A nontrivial example is also provided to support the results. The results generalize, improve, and extend existing results in the literature.
