Mathematics
(MDPI (Basel, Switzerland))
• 01 Apr 2020
Baradol, Pravin • Vujaković, Jelena • Gopal, Dhananjay • Radenović, Stojan
In this paper, we provide an approach to establish the Banach contraction principle (for the case λ∈[0,1)) , Edelstein, Reich, and Meir–Keeler type contractions in the context of graphical rectangular b-metric space. The obtained results not only enrich and improve recent fixed point theorems of this new metric spaces but also provide positive answers to the questions raised by Mudasir Younis et al. (J. Fixed Point Theory Appl., doi:10.1007/s11784-019-0673-3, 2019).
Mathematics
(MDPI (Basel, Switzerland))
• 11 May 2020
Vujaković, Jelena • Mitrović, Slobodanka • Pavlović, Mirjana • Radenović, Stojan
In this manuscript we discuss, consider, generalize, improve and unify several recent results for so-called F-contraction-type mappings in the framework of complete metric spaces. We also introduce (φ,F) -weak contraction and establish the corresponding fixed point result. Using our new approach for the proof that a Picard sequence is a Cauchy in metric space, our obtained results complement and enrich several methods in the existing literature. At the end we give one open question for F-contrac ...
Mathematics
(MDPI (Basel, Switzerland))
• 21 Sep 2020
Vujaković, Jelena • Mitrović, Slobodanka • Mitrović, Zoran • Radenović, Stojan
In the paper, we consider some fixed point results of F-contractions for triangular α-admissible and triangular weak α-admissible mappings in metric-like spaces. The results on F-contraction type mappings in the context of metric-like spaces are generalized, improved, unified, and enriched. We prove the main result but using only the property (F1) of the strictly increasing mapping F:(0,,,+,∞)→(−,∞,,,+,∞). Our approach gives a proper generalization of several results given in current literature.
Mathematics
(MDPI (Basel, Switzerland))
• 07 Jan 2021
Vujaković, Jelena • Ljajko, Eugen • Pavlović, Mirjana • Radenović, Stojan
One of the main goals of this paper is to obtain new contractive conditions using the method of a strictly increasing mapping F:(0,+∞)→(−∞,+∞). According to the recently obtained results, this was possible (Wardowski’s method) only if two more properties (F2) and (F3) were used instead of the aforementioned strictly increasing (F1). Using only the fact that the function F is strictly increasing, we came to new families of contractive conditions that have not been found in the existing literature ...
Mathematics
(MDPI (Basel, Switzerland))
• 12 Aug 2021
Mitrović, Slobodanka • Parvaneh, Vahid • De la Sen, Manuel • Vujaković, Jelena • Radenović, Stojan
In this article, we generalize, improve, unify and enrich some results for Jaggi-W-contraction-type mappings in the framework of b-metric-like spaces. Our results supplement numerous methods in the existing literature, and we created new approach to prove that a Picard sequence is Cauchy in a b-metric-like space. Among other things, we prove Wardowski’s theorem, but now by using only the property (W1). Our proofs in this article are much shorter than ones in recently published papers.
Mathematics
(MDPI (Basel, Switzerland))
• 21 Dec 2021
Vujaković, Jelena • Kontrec, Nataša • Tošić, Marina • Fabiano, Nicola • Radenović, Stojan
The main purpose of this paper is to improve, generalize, unify, extend and enrich the recent results established by Dung and Hang (2015), Piri and Kumam (2014, 2016), and Singh et al. (2018). In our proofs, we only use the property (F1) of Wardowski’s F-contraction, while the many authors in their papers still use all tree properties of F-contraction as well as two new properties introduced by Piri and Kumam. Our approach in this paper indicates that for most results with F-contraction, propert ...
UNITECH 2018, International Scientific Conference, 16-17 November, Gabrovo 2018, Bulgaria
(TECHNICAL UNIVERSITY OF GABROVO, 2018 UNIVERSITY PUBLISHING HOUSE “V. APRILOV” – GABROVO, 2018)
• 01 Apr 2024
Vujaković, Jelena • Panić, Stefan • Kontrec, Nataša
In real iterations, several types of mean value theorems for definite integrals are used. In complex domain, we cannot specifically formulate the mean value theorem of a particular complex line integral (L) ∫f(z)dz , since we are unable to give an appropriate geometric interpretation of the integral over the surface below a curve L (from z0 to z1 ). Based on the
mean value theorems for a complex line integral in [Vujakovic J., The mean value theorem of line complex integral and Sturm functio ...
UNITECH 2018, International Scientific Conference, 16-17 November, Gabrovo 2018, Bulgaria
(TECHNICAL UNIVERSITY OF GABROVO, 2018 UNIVERSITY PUBLISHING HOUSE “V. APRILOV” – GABROVO, 2018)
• 01 Apr 2024
Vujaković, Jelena • Kontrec, Nataša • Panić, Stefan
The theory of complex differential equations represents an important mathematical discipline both from the theoretical point of view and from numerous applications. Its development was equally encouraged by mathematicians, physicists and engineers. By using the series-iterations method we have explained how the obtained results could be
applied to the complex linear homogeneous first order and canonical complex linear second order differential equations. We have also formulated some conclusi ...
International Scientific Conference UNITECH 2019, Gabrovo, 15-16 November 2019, Bulgaria
(TECHNICAL UNIVERSITY OF GABROVO, 2019 UNIVERSITY PUBLISHING HOUSE “V. APRILOV” – GABROVO, 2019)
• 01 Apr 2024
Vujaković, Jelena • Kontrec • Panić, Stefan
The problem of location of the zero solution of the second order complex oscillator equation for the given analytic function is unlikely to be completely solved. Therefore, estimates have long been resorted to. The easiest case is if the zeros are aligned at the same direction, which is rare. Since there are no other zeros between the two directions, we will assume that there are many zeros on practically every direction in the sector
International Scientific Conference UNITECH 2019, Gabrovo, 15-16 November 2019, Bulgaria
(TECHNICAL UNIVERSITY OF GABROVO, 2019 UNIVERSITY PUBLISHING HOUSE “V. APRILOV” – GABROVO, 2019)
• 01 Apr 2024
Vujaković, Jelena • Jovanović, Tanja • Kontrec, Nataša
By solving the frequency function equation only a small number of complex equations of the second order oscillations can be solved. The simplest way is to observe canonical complex differential equations with constant coefficient. In this paper we give an overview of eight cases of complex differential equations in which the coefficient is a polynomial or a variable coefficient
