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Mihai Turinici

Publications and source records attributed to Mihai Turinici.

At least 19 recordsLinked to original sources
arXiv2026

JAI functional contractions in relational metric spaces

The 2015 fixed point result on rs-relational metric spaces due to Alam and Imdad [J. Fixed Point Th. Appl., 17 (2015), 693-702] is equivalent with the classical Banach Contraction Principle [Fund. Math., 3 (1922), 133-181]. This is also valid for the 1961 statement in metric spaces due to Edelstein [Proc. Amer. Math. Soc., 12 (1961), 7-10], or the 2005 fixed point result in quasi-ordered metric spaces obtained by Nieto and Rodriguez-Lopez [Order, 22 (2005), 223-239].

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arXiv2015

Ultrametric fixed points in reduced axiomatic systems

The Brezis-Browder ordering principle [Advances Math., 21 (1976), 355-364] is used to get a proof, in the reduced axiomatic system (ZF-AC+DC), of a fixed point result [in the complete axiomatic system (ZF)] over Cantor complete ultrametric spaces due to Petalas and Vidalis [Proc. Amer. Math. Soc., 118 (1993), 819-821].

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arXiv2014

PPF dependent fixed points in A-closed Razumikhin classes

The PPF dependent fixed point result in algebraically closed Razumikhin classes due to Agarwal et al [Fixed Point Theory Appl., 2013, 2013:280] is identical with its constant class counterpart; and this, in turn, is reducible to a fixed point principle involving SVV type contractions (over the subsequent metric space of initial Banach structure), without any regularity conditions about the Razumikhin classes. The conclusion remains valid for all PPF dependent fixed point results founded on such global conditions.

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arXiv2013

Contractive maps in locally transitive relational metric spaces

Some fixed point results are given for a class of Meir-Keeler contractive maps acting on metric spaces endowed with locally transitive relations. Technical connections with the related statements due to Berzig et al [Abstr. Appl. Anal., Volume 2013, Article ID 259768] are also being discussed.

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arXiv2013

Function contractive maps in triangular symmetric spaces

Some fixed point results are given for a class of functional contractions acting on (reflexive) triangular symmetric spaces. Technical connections with the corresponding theories over (standard) metric and partial metric spaces are also being established.

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arXiv2013

Weakly contractive maps in altering metric spaces

The weakly contractive metric type fixed point result in Berinde [Nonlinear Anal. Forum, 9 (2004), 45-53] is "almost" covered by the related altering metric one due to Khan et al [Bull. Austral. Math. Soc., 30 (1984), 1-9]. Further extensions of these statements are then provided.

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arXiv2013

Contractive maps in Mustafa-Sims metric spaces

The fixed point result in Mustafa-Sims metrical structures obtained by Karapinar and Agarwal [Fixed Point Th. Appl., 2013, 2013:154] is deductible from a corresponding one stated in terms of anticipative contractions over the associated (standard) metric space.

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arXiv2013

Implicit contractive maps in ordered metric spaces

Further extensions are given to the fixed point result (for implicit contractions) due to Altun and Simsek [Fixed Point Th. Appl., Volume 2010, Article ID 621469]. Some connections with related statements in the area due to Agarwal, El-Gebeily and O'Regan [Appl. Anal., 87 (2008), 109-116] are also discussed. Finally, the old approach in Turinici [An. St. Univ. "A. I. Cuza" Iasi, 22 (1976), 177-180] is presented, for historical reasons.

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arXiv2013

Gauge Brezis-Browder Principles and Dependent Choice

The gauge Brezis-Browder Principle in Turinici [Bull. Acad. Pol. Sci. (Math.), 30 (1982), 161-166] is obtainable from the Principle of Dependent Choices (DC) and implies Ekeland's Variational Principle (EVP); hence, it is equivalent with both (DC) and (EVP). This is also true for the gauge variational principle deductible from it, including the one in Bae, Cho, and Kim [Bull. Korean Math. Soc. 48 (2011), 1023-1032].

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arXiv2013

Variational Principles in Fang Uniform Spaces

The vectorial Zhu-Li Variational Principle (ZLVP) in Fang uniform spaces is in the logical segment between the Brezis-Browder ordering principle (BB) and Ekeland's Variational Principle (EVP); hence, it is equivalent with both BB and EVP. In particular, the conclusion is applicable to Hamel's Variational Principle (HVP). Finally, a proof of [HVP equivalent with EVP] is provided, by means of a direct approach.

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arXiv2012

Function contractive maps in partial metric spaces

Some fixed point results are given for a class of functional contractions over partial metric spaces. These extend some contributions in the area due to Ilic et al [Math. Comput. Modelling, 55 (2012), 801-809].

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arXiv2011

Product fixed points in ordered metric spaces

All product fixed point results in ordered metric spaces based on linear contractive conditions are but a vectorial form of the fixed point statement due to Nieto and Rodriguez-Lopez [Order, 22 (2005), 223-239], under the lines in Matkowski [Bull. Acad. Pol. Sci. (Ser. Sci. Math. Astronom. Phys.), 21 (1973), 323-324].

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arXiv2011

Nonlinear Versions of a Vector Maximal Principle

Some nonlinear extensions of the vector maximality statement established by Goepfert, Tammer and Zalinescu [Nonl. Anal., 39 (2000), 909-922] are given. Basic instruments for these are the Brezis-Browder ordering principle [Advances Math., 21 (1976), 355-364] and a (pseudometric) version of it obtained in Turinici [Demonstr. Math., 22 (1989), 213-228].

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arXiv2011

Ran-Reurings theorems in ordered metric spaces

The Ran-Reurings fixed point theorem [Proc. Amer. Math. Soc., 132 (2004), 1435-1443] is but a particular case of Maia's [Rend. Sem. Mat. Univ. Padova, 40 (1968), 139-143]. A "functional" version of this last result is then provided, in a convergence-metric setting.

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arXiv2011

Nieto-Lopez theorems in ordered metric spaces

The comparison type version of the fixed point result in ordered metric spaces established by Nieto and Rodriguez-Lopez [Acta Math. Sinica (English Series), 23 (2007), 2205-2212] is nothing but a particular case of the classical Banach's contraction principle [Fund. Math., 3 (1922), 133-181].

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