Search

In this paper, we introduce the concept of (F, G)-perturbed contraction in a metric space and we establish some fixed point theorems which extends the results from Branga, A. N. Olaru, I. M. Some Fixed Point Results in Spaces with Perturbed Metrics. Carpathian J. Math. 38 (2022), no. 3, 641–654 and Olaru, I. M.; Secelean, N. A. A new approach of some contractive mappings on metric spaces. Mathematics 9 (2021), 1433. Also, an application to an integral equation and some illustrative examples are given throughout the paper. [ABSTRACT FROM AUTHOR]

In this paper we give some fixed point theorems for nonself generalized contractions on a large Kasahara space, which generalize some results given by I.A. Rus and M.-A. S¸erban (I.A. Rus, M.-A. S¸erban, Some fixed point theorems for nonself generalized contractions, Miskolc Math. Notes, 17(2016), no.2, 1021-1031) and by S. Reich and A.J. Zaslavski (S. Reich, A.J. Zaslavski, A note on Rakotch contractions, Fixed Point Theory, 9(2008), no.1, 267-273) in complete metric spaces. We prove our results without using the completeness of the metric structure. [ABSTRACT FROM AUTHOR]

In this paper, we prove convergence theorems for a fixed point iterative algorithm of Krasnoselskij- Mann type associated to the class of enriched nonexpansive mappings in Banach spaces. The results are direct generalizations of the corresponding ones in [Berinde, V., Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces, Carpathian J. Math., 35 (2019), No. 3, 293-304.], from the setting of Hilbert spaces to Banach spaces, and also of some results in [Senter, H. F. and Dotson, Jr., W. G., Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc., 44 (1974), No. 2, 375-380.], [Browder, F. E., Petryshyn, W. V., Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl., 20 (1967), 197-228.], by considering enriched nonexpansive mappings instead of nonexpansive mappings. Many other related results in literature can be obtained as particular instances of our results. [ABSTRACT FROM AUTHOR]

A class of demicontractive mappings was first introduced in [Hicks, T. L. and Kubicek, J. D., On the Mann iteration process in a Hilbert space, J. Math. Anal. Appl., 59 (1977) 498-504 and Maruster, S., The solution by iteration of nonlinear equations in Hilbert spaces, Proc. Amer. Math. Soc., 63 (1977), 69-73] and was first mentioned in the case of multi-valued mappings in [Chidume, C. E., Bello, A. U. and Ndambomve, P., Strong and δ-convergence theorems for common fixed points of a finite family of multivalued demicontractive mappings in CAT(0) spaces, Abstr. Appl. Anal., 2014 (2014), https://doi.org/10.1155/2014/805168 and Isiogugu, F. O. and Osilike, M. O., Convergence theorems for new classes of multivalued hemicontractive-type mappings, Fixed Point Theory Appl., 2014 (2014), https://doi.org/10.1186/1687-1812-2014-93]. The demicontractivity with some weak smoothness conditions ensures only weak convergence of Mann iteration. In 2015, Marus,ter and Rus [Kannan contractions and strongly demicontractive mappings, Creat. Math. Inform., 24 (2015), No. 2, 173-182], introduced a class of strongly demicontractive mappings, and also discussed some relationships between strongly demicontractive mappings and Kannan contractions. In this paper, we introduce a new class of strongly demicontractive multivalued mappings in Hilbert spaces. Strong convergence theorems of Picard and Mann iterative methods for strongly demicontractive multi-valued mappings are established under some suitable coefficients and control sequences. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept of Ulam stability of fixed point equation with respected to a directed graph. Two fixed point theorems of Matkowski and of Jachymski are discussed further in the sense of this stability concept. Some examples about the validity of our notion are given. Finally, we discuss the vagueness of the recent stability results of Sintunavarat [Sintunavarat, W., A new approach to α-ψ -contractive mappings and generalized Ulam-Hyers stability, well-posedness and limit shadowing results, Carpathian J. Math., 31 (2015), 395-401]. [ABSTRACT FROM AUTHOR]

In this paper we present two new results for the existence of fixed points of multivalued mappings with closed values on quasi metric space. First we introduce the multivalued Fd-contraction on quasi metric space (X; d) and give a fixed point result related to this concept. Then taking into account the Q-function on a quasi metric space, we establish a Q-function version of this concept as multivalued Fq-contraction and hence we present a fixed point result to see the effect of Q-function to existence of fixed point of multivalued mappings on quasi metric space. [ABSTRACT FROM AUTHOR]

Following a well established tradition of marking the main anniversary moments of the journal by an editorial, see the previous ones: [Berinde, V., Anniversary: Ten years of publication of the new series of Buletin S, tiint,ific, Bul. S,tiint,. Univ. Baia Mare, Ser. B., Matematica-Informatica, 16 (2000), No. 1, i-ii], [Berinde, V., Carpathian Journal of Mathematics: Celebrating 20 years of publication of the new series, Carpathian J. Math., 21 (2010), No. 2, i-vi], [Berinde, V., CJM celebrates 25 years of publication of its new series, Carpathian J. Math., 26 (2015), No. 3, i-vi], it is the main aim of this note to present a brief account of what has been achieved since the previous anniversary editorial written five years ago. [ABSTRACT FROM AUTHOR]

In this paper we study some approximation properties of a sequence of positive linear operators defined by means of the powered Baskakov basis. We prove that in the particular case of squared Baskakov basis the operators behave better than the classical Baskakov operators. For this particular case we give also a quantitative Voronovskaya type result. [ABSTRACT FROM AUTHOR]

Using the concept of the CATp(0) spaces proposed by Khamsi et al. [Khamsi, M. A. and Shukri, S. A., Generalized CAT(0) spaces. Bull. Belg. Math. Soc. Simon Stevin, 24 (2017), No. 3, 417-426], we establish Δ-convergence and strong convergence of a perturbed variant of Agarwal et al. S-iteration process for nonexpansive mapping. Finally, from them we deduce results valid for α-nonexpansive mappings. [ABSTRACT FROM AUTHOR]

We consider the skew Laplacian matrix of a digraph G obtained by giving an arbitrary direction to the edges of a graph G having n vertices and m edges. We obtain an upper bound for the skew Laplacian spectral radius in terms of the adjacency and the signless Laplacian spectral radius of the underlying graph G. We also obtain upper bounds for the skew Laplacian spectral radius and skew spectral radius, in terms of various parameters associated with the structure of the digraph G and characterize the extremal graphs. [ABSTRACT FROM AUTHOR]

Professor Emeritus Ioan A. Rus, a prominent and unfatiguable mathematician with an impressive oeuvre in the field of Nonlinear Analysis, particularly in Fixed Point Theory, will be 80 on 28th of August 2016. On this occasion, we would like to congratulate him and wish him good health, happiness, the same impressive physical and mental vigour, as well as new bright results in mathematics. We also take this opportunity to present some information on the visibility and impact of Professor Rus' main scientific contributions, which would thus complement the information given in the following anniversary articles [ABSTRACT FROM AUTHOR]