Browsing by Author "Kumar, Santosh"
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Item (alpha, beta) -Lp 2 -norm orthogonality and characterizations of 2 - inner product spaces,(Eudoxus Press, LLC of TN, 2008) Vinai, K. Singh; Kumar, Santosh; Singh, A. K.In the present paper we have characterised (alpha, beta, )−Lp orthogonality in a 2- normed linear space. In some way the results proved in this paper generalize some of the similar characterization of generalized Lp- orthogonality derived earlier by Zheng Liu[8].Item Approximating fixed point of generalized nonexpansive mappings(ASCENT PUBLICATION, 2012) Kumar, SantoshUnder certain conditions the convergence of Ishikawa iterate to a unique xed point is proved for nonexpansive type mappings in a uniformly convex Banach space. In this paper we improve the results given by Pathak and Khan [6].Item COMMON FIXED POINT FOR A PAIR OF NON-SELF MAPPINGS IN PARTIAL METRIC SPACES(Busan International Nonlinear Analysis Academy, 2017-06) Rugumisa, Terentius; Kumar, SantoshIn this paper we prove a common fixed point theorem for a pair of non-self mappings in partial metric spaces. We generalize a theorem by Imdad and Kumar which was proved for metric spaces. We also provide an illustrative example.Item COMMON FIXED POINTS FOR FOUR NON-SELF-MAPPINGS(Vijñāna Parishad of India: Jnanabha, 2017-12) Kumar, Santosh; Rugumisa, TerentiusIn this paper, we formulate a quasi-contraction type non-self mapping on Takahashi convex metric spaces and common fixed point theorems that applies to two pairs of mappings. The result generalizes the fixed point theorems of some previous authorsItem COMMON FIXED POINTS FOR FOUR NON-SELF-MAPPINGS IN PARTIAL METRIC SPACES(Mathematica Bohemica, 2018) Terentius, Rugumisa; Kumar, Santosh; Mohammad, ImdadIn this paper, we formulate a common fi xed point theorem for four non-self mappings in convex partial metric spaces. The result extends a fi xed point theorem by Gajic and Rakocevic [Pair of non-self mappings and common fi xed points. Appl. Math. Comp. 187 (2007), 999-1006] proved for two non-self mappings in metric spaces with a Takahashi convex structure. We also provide an illustrative example on the use of the theorem.Item COMMON FIXED POINTS IN METRICALLY CONVEX PARTIAL METRIC SPACES(Dergi Konuralp Journal of Mathematics, 2017-12) Kumar, Santosh; Rugumisa, Terentius; Imdad, Mohd.In this study, we extend some common xed points theorems for mappings in metrically convex metric spaces into partial metric spaces. We generalize earlier results by Imdad et al. We also provide an illustrative example.Item Common fixed points of a pair of multivalued non-self mappings in partial metric spaces(Malaya Journal of Matematik, 2018, 2018-07-01) Kumar, Santosh; Rugumisa, TerentiusIn this paper, we utilize the concept of the partial Hausdorff metric, first introduced by Aydi et al.[4] for partial metric space, to consider a pair of multivalued mappings which are non-self almost contractions on metrically convex partial metric spaces. We establish the existence of fixed point in such mappings.Item COMMON FIXED POINTS OF HYBRID PAIRS OF NON-SELF MAPPINGS SATISFYING AN IMPLICIT RELATION IN PARTIAL METRIC SPACES(Aligarh Muslim University, Aligarh, India, 2017) Kumar, Santosh; Kessy, JohnsonIn this paper, we define a hybrid-type tangential property in the sense of Ahmed [8] in the setting of partial metric spaces. We obtain some results for coincidence and common fixed points of two hybrid pairs of non-self mappings satisfying an implicit relation due to Popa [19] under the tangential property in a partial metric space. Our results unify and generalize some existing ones in the literature.Item An Eco-epidemiological Model for Newcastle Disease in Central Zone of Tanzania(Inder Science Publishers, 2017) Hugo, Alfred; Oluwole, Daniel Makinde; Kumar, SantoshNewcastle disease is contagious bird disease which affects main domestic and wild avian species. A deterministic compartmental model for Newcastle disease (ND) is developed and analysed using ordinary differential equation theory. The uncertainties of model parameters were therefore examined using Markov Chain Monte Carlo (MCMC) simulations for the data of chicken death cases due to Newcastle disease from five districts in two regions in Tanzania. The parameter distribution was tested using MCMC convergence diagnostics. The graphical diagnostic test for MCMC used include Trace plots or time series plot, two-dimensional parameter plots and autocorrelation function plots. Hence, model parameters were successfully estimated for numerical simulations and the results of simulations were presented.Item Fixed Point Theorem for F-contraction Mappings, in Partial Metric Spaces(Pleiades Publishing, Ltd., 2019-03-01) Luambano, Sholastica; Kumar, Santosh; Kakiko, GraysonThe purpose of this paper is to establish a fixed point theorem for F-contraction mappings in partial metric spaces. Also, as a consequence, a fixed point theorem for a pair of F-contraction mappings having a unique common fixed point is obtained. In particular, the main results in this paper generalize and extend a fixed point theorem due to Wardowski 2012 in which F-contraction was introduced as a generalization of Banach Contraction Principle. An illustrative example is provided to validate the results.Item FIXED POINTS FOR HYBRID MAPPINGS SATISFYING AN IMPLICIT RELATION IN PARTIAL METRIC SPACES(Jnanabha-Vijñāna Parishad of India, 2018-12-01) Kumar, Santosh; Rugumisa, TerentiusIn this paper, we prove a fi xed point theorem for hybrid mappings in partial metric spaces. The theorem contains an altering distance function and involves an implicit relation satisfying the (E.A) - property. In doing so, we generalize a theorem by Popa and Patriciu.Item FIXED POINTS FOR HYBRID PAIR OF COMPATIBLE MAPPINGS IN PARTIAL METRIC SPACES(Scik.org, 2017) Johnson, Kessy; Kumar, Santosh; Kakiko, GraysonIn this paper coincidence and fixed point theorems for a pair of single-valued and multi-valued compatible mappings on complete partial metric spaces are presented. The notion of compatible mappings for a pair of single-valued and multi-valued mappings proved to be very useful as the existing metric fixed point theory contains numerous fixed point results for pair(s) of mappings established under compatibility condition and its generalizations. Partial metric spaces are one of generalizations of the notion of a metric space that allows non-zero self distance. The existing metric fixed point theory approaches, are adapted to establish the results. The main result generalizes, in particular, a fixed point theorem due to Kaneko and Sessa for hybrid pair of compatible mappings. An illustrative example is also provided.Item Fixed points for non-self mappings in multiplicative metric spaces(Malaya Journal of Matematik, Vol. 6, No. 4, 800-806, 2018, 2018-07-01) Kumar, Santosh; Rugumisa, TerentiusIn this paper, we develop a theorem for a pair of non-self mappings. For this purpose, we define a multiplicative convex metric space and state the condition for a mapping in such space to have a fixed point. We explain the procedure of locating the fixed point. We also provide an illustrative example on the use of the theorem.Item Fixed Points of Non-Self Mappings in Partial Metric Spaces(Natural Sciences Publishing: Journal of Analysis & Number Theory, 2018-01) Rugumisa, Terentius; Kumar, SantoshA number of theorems on contractive mappings for common fixed points in partial metric spaces have been proved and many of them apply to self maps. In this paper, we extend a common fixed point theorem on a partial metric space by Karapinar et al. so that it can apply to a non-self mapping in a metrically convex partial metric space under specified conditions.Item AN IMPLICIT RELATION FOR FOUR NON-SELF MAPPINGS IN PARTIAL METRIC SPACES(Jnanabha-Vijñāna Parishad of India, 2017-06) Kumar, Santosh; Rugumisa, TerentiusBerinde and Vetro (2012) introduced fixed points theorems involving implicit relations for metric spaces and ordered metric spaces. These theorems were extended into partial metric spaces by other researchers. Vetro and Vetro studied coincidence point and common fixed point theorems for one pair of self-mappings satisfyirg conditions defined by implicit relations in the settings of partial metric space. We extend these results by Vetro and Vetro to two pairs of non-self mappings in complete partiai metric spaces having a convex structure.Item Iteration process with errors for local strongly Haccretive type mappings(Casa Cărţii de Ştiinţă Cluj- Napoca(House of the Book of Science Cluj- Napoca)Eroilor street 6-8, 400129 Cluj- Napoca ROMANIA, 2008) Vinai, K. Singh; Kumar, SantoshSome iteration processes of Mann and Ishikawa type with error has been discussed to approximate solution of equation Tx = f, where T is locally strongly H - accretive mapping [1 8] on uniformly smooth Banach space X. This extends an earlier result of Liu [9]on iterative processes with errors. We also extend a result of Weng [20] on iterative processes of dissipative type mappings.Item Mapping Phi-p in normed linear spaces and characterization of orthogonality problem of best approximation in 2-norm(Lucian Blaga" Univer sity Of Sibiu - Faculty Of Science -Department Of Mathematics, 2009) Vinai, K. Singh; Kumar, SantoshIn order to characterizations of best approximations have been given in 2-norm space (X, || .,|| ). Some generalization of the function phi-p of Dragomir type have been given in the context where the said generalization help to formulate the characterizations what have been proposed in this article.Item A Note on a Fixed Point Theorem(2013-01) Kumar, SantoshIn this paper we gave a simple extension of a fixed point theorem for non-expansive maps.We derives several known results e.g. [3,4,6] as corollaries.Item A note on a fixed point theorem(Scik.org, 2013) Kumar, SantoshIn this paper we gave a simple extension of a xed point theorem for non-expansive maps. We derives several known results e.g. [3,4,6] as corollaries.Item Optimal Control and Cost Effectiveness Analysis for Newcastle Disease Eco- Epidemiological Model in Tanzania(Taylor & Francis-J. Biological Dynamics, 2016) Hugo, Alfred; Oluwole, Daniel Makinde; Kumar, Santosh; Fred, ChibwanaIn this paper, a deterministic compartmental eco- epidemiological model with optimal control of Newcastle disease (ND) in Tanzania is proposed and analysed. Necessary conditions of optimal control problem were rigorously analysed using Pontryagin’s maximum principle and the numerical values of model parameters were estimated using maximum likelihood estimator. Three control strategies were incorporated such as chicken vaccination (preventive), human education campaign and treatment of infected human (curative) and its’ impact were graphically observed. The incremental cost effectiveness analysis technique used to determine the most cost effectiveness strategy and we observe that combination of chicken vaccination and human education campaign strategy is the best strategy to implement in limited resources. Therefore,NDcan be controlled if the farmers will apply chicken vaccination properly and well in time.